Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1568,2,Mod(177,1568)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1568, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1568.177");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.t (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.5205430369\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.432972864.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + x^{6} + 4x^{5} - 6x^{4} + 8x^{3} + 4x^{2} - 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 177.1 | ||
Root | \(0.630783 + 1.26575i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1568.177 |
Dual form | 1568.2.t.d.753.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(1471\) | \(1473\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.61578 | + | 1.51022i | −1.51022 | + | 0.871928i | −0.510295 | + | 0.859999i | \(0.670464\pi\) |
−0.999929 | + | 0.0119288i | \(0.996203\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.46890 | + | 0.848071i | 0.656913 | + | 0.379269i | 0.791100 | − | 0.611687i | \(-0.209509\pi\) |
−0.134187 | + | 0.990956i | \(0.542842\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.06155 | − | 5.30277i | 1.02052 | − | 1.76759i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.14688 | − | 0.662153i | 0.345798 | − | 0.199647i | −0.317035 | − | 0.948414i | \(-0.602687\pi\) |
0.662833 | + | 0.748767i | \(0.269354\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.69614i | 0.470425i | 0.971944 | + | 0.235212i | \(0.0755786\pi\) | ||||
−0.971944 | + | 0.235212i | \(0.924421\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.12311 | −1.32278 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | − | 1.73205i | −0.242536 | − | 0.420084i | 0.718900 | − | 0.695113i | \(-0.244646\pi\) |
−0.961436 | + | 0.275029i | \(0.911312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.61578 | + | 1.51022i | 0.600102 | + | 0.346469i | 0.769082 | − | 0.639150i | \(-0.220714\pi\) |
−0.168980 | + | 0.985620i | \(0.554047\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.56155 | − | 4.43674i | 0.534121 | − | 0.925124i | −0.465085 | − | 0.885266i | \(-0.653976\pi\) |
0.999205 | − | 0.0398580i | \(-0.0126905\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.06155 | − | 1.83866i | −0.212311 | − | 0.367733i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 9.43318i | 1.81542i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.04090i | − | 1.12177i | −0.827895 | − | 0.560883i | \(-0.810462\pi\) | ||
0.827895 | − | 0.560883i | \(-0.189538\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.12311 | − | 8.87348i | −0.920137 | − | 1.59372i | −0.799201 | − | 0.601064i | \(-0.794744\pi\) |
−0.120936 | − | 0.992660i | \(-0.538589\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.00000 | + | 3.46410i | −0.348155 | + | 0.603023i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.23157 | − | 3.02045i | −0.860065 | − | 0.496559i | 0.00396926 | − | 0.999992i | \(-0.498737\pi\) |
−0.864034 | + | 0.503434i | \(0.832070\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.56155 | − | 4.43674i | −0.410177 | − | 0.710447i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.24621 | 0.663147 | 0.331573 | − | 0.943429i | \(-0.392421\pi\) | ||||
0.331573 | + | 0.943429i | \(0.392421\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.32431i | 0.201955i | 0.994889 | + | 0.100977i | \(0.0321970\pi\) | ||||
−0.994889 | + | 0.100977i | \(0.967803\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.99424 | − | 5.19283i | 1.34078 | − | 0.774101i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.23157 | + | 3.02045i | 0.732566 | + | 0.422947i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.29377 | + | 1.32431i | −0.315073 | + | 0.181908i | −0.649194 | − | 0.760623i | \(-0.724894\pi\) |
0.334121 | + | 0.942530i | \(0.391560\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.24621 | 0.302879 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.12311 | −1.20838 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.322018 | − | 0.185917i | 0.0419231 | − | 0.0242043i | −0.478892 | − | 0.877874i | \(-0.658961\pi\) |
0.520815 | + | 0.853670i | \(0.325628\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.46890 | − | 0.848071i | −0.188074 | − | 0.108584i | 0.403007 | − | 0.915197i | \(-0.367965\pi\) |
−0.591080 | + | 0.806613i | \(0.701298\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.43845 | + | 2.49146i | −0.178417 | + | 0.309028i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.96029 | − | 5.75058i | 1.21684 | − | 0.702545i | 0.252602 | − | 0.967570i | \(-0.418714\pi\) |
0.964241 | + | 0.265026i | \(0.0853804\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 15.4741i | 1.86286i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.00000 | + | 5.19615i | 0.351123 | + | 0.608164i | 0.986447 | − | 0.164083i | \(-0.0524664\pi\) |
−0.635323 | + | 0.772246i | \(0.719133\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.55359 | + | 3.20636i | 0.641273 | + | 0.370239i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.06155 | − | 8.76687i | −0.562395 | − | 0.974096i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.66906i | 0.622260i | 0.950367 | + | 0.311130i | \(0.100708\pi\) | ||||
−0.950367 | + | 0.311130i | \(0.899292\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 3.39228i | − | 0.367945i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.12311 | + | 15.8017i | 0.978100 | + | 1.69412i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.12311 | − | 14.0696i | 0.861047 | − | 1.49138i | −0.00987147 | − | 0.999951i | \(-0.503142\pi\) |
0.870919 | − | 0.491427i | \(-0.163524\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 26.8019 | + | 15.4741i | 2.77923 | + | 1.60459i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.56155 | + | 4.43674i | 0.262810 | + | 0.455200i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.2462 | 1.24341 | 0.621707 | − | 0.783250i | \(-0.286439\pi\) | ||||
0.621707 | + | 0.783250i | \(0.286439\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 8.10887i | − | 0.814972i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.99424 | + | 5.19283i | −0.894960 | + | 0.516705i | −0.875562 | − | 0.483106i | \(-0.839508\pi\) |
−0.0193984 | + | 0.999812i | \(0.506175\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.12311 | − | 1.94528i | 0.110663 | − | 0.191674i | −0.805375 | − | 0.592766i | \(-0.798036\pi\) |
0.916038 | + | 0.401092i | \(0.131369\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.2541 | + | 7.07488i | 1.18464 | + | 0.683955i | 0.957084 | − | 0.289809i | \(-0.0935919\pi\) |
0.227560 | + | 0.973764i | \(0.426925\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.6947 | − | 9.06134i | 1.50328 | − | 0.867919i | 0.503288 | − | 0.864119i | \(-0.332124\pi\) |
0.999993 | − | 0.00380035i | \(-0.00120969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18.2462 | 1.73185 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.87689 | 0.458780 | 0.229390 | − | 0.973335i | \(-0.426327\pi\) | ||||
0.229390 | + | 0.973335i | \(0.426327\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.52534 | − | 4.34475i | 0.701741 | − | 0.405150i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.99424 | + | 5.19283i | 0.831518 | + | 0.480077i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.62311 | + | 8.00745i | −0.420282 | + | 0.727950i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.1072 | + | 6.41273i | −1.00150 | + | 0.578216i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 12.0818i | − | 1.08063i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.1231 | −1.16449 | −0.582244 | − | 0.813014i | \(-0.697825\pi\) | ||||
−0.582244 | + | 0.813014i | \(0.697825\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.00000 | − | 3.46410i | −0.176090 | − | 0.304997i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.7852 | − | 6.22681i | −0.942303 | − | 0.544039i | −0.0516218 | − | 0.998667i | \(-0.516439\pi\) |
−0.890682 | + | 0.454628i | \(0.849772\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.00000 | + | 13.8564i | −0.688530 | + | 1.19257i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.12311 | + | 14.0696i | 0.694004 | + | 1.20205i | 0.970515 | + | 0.241039i | \(0.0774882\pi\) |
−0.276512 | + | 0.961011i | \(0.589178\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 8.31768i | − | 0.705496i | −0.935718 | − | 0.352748i | \(-0.885247\pi\) | ||
0.935718 | − | 0.352748i | \(-0.114753\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.12311 | + | 1.94528i | 0.0939188 | + | 0.162672i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.12311 | − | 8.87348i | 0.425451 | − | 0.736902i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.7569 | − | 7.36520i | −1.04509 | − | 0.603381i | −0.123817 | − | 0.992305i | \(-0.539513\pi\) |
−0.921270 | + | 0.388924i | \(0.872847\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.43845 | + | 9.41967i | 0.442575 | + | 0.766562i | 0.997880 | − | 0.0650850i | \(-0.0207319\pi\) |
−0.555305 | + | 0.831647i | \(0.687399\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.2462 | −0.990048 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 17.3790i | − | 1.39592i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.34451 | − | 4.24035i | 0.586155 | − | 0.338417i | −0.177420 | − | 0.984135i | \(-0.556775\pi\) |
0.763576 | + | 0.645718i | \(0.223442\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.00000 | − | 6.92820i | 0.317221 | − | 0.549442i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.6100 | − | 6.70305i | −0.909367 | − | 0.525023i | −0.0291396 | − | 0.999575i | \(-0.509277\pi\) |
−0.880227 | + | 0.474552i | \(0.842610\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.87560 | + | 3.39228i | −0.457415 | + | 0.264089i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.00000 | −0.619059 | −0.309529 | − | 0.950890i | \(-0.600171\pi\) | ||||
−0.309529 | + | 0.950890i | \(0.600171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.1231 | 0.778700 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.0167 | − | 9.24726i | 1.22483 | − | 0.707156i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.5196 | − | 9.53758i | −1.25596 | − | 0.725129i | −0.283673 | − | 0.958921i | \(-0.591553\pi\) |
−0.972287 | + | 0.233792i | \(0.924886\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.561553 | + | 0.972638i | −0.0422089 | + | 0.0731079i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.08469 | − | 2.35829i | 0.305304 | − | 0.176267i | −0.339519 | − | 0.940599i | \(-0.610264\pi\) |
0.644823 | + | 0.764332i | \(0.276931\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.99337i | 0.519813i | 0.965634 | + | 0.259906i | \(0.0836917\pi\) | ||||
−0.965634 | + | 0.259906i | \(0.916308\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.12311 | 0.378711 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.12311 | − | 8.87348i | −0.376658 | − | 0.652391i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.29377 | − | 1.32431i | −0.167737 | − | 0.0968429i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.00000 | − | 13.8564i | 0.578860 | − | 1.00261i | −0.416751 | − | 0.909021i | \(-0.636831\pi\) |
0.995610 | − | 0.0935936i | \(-0.0298354\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.56155 | + | 9.63289i | 0.400329 | + | 0.693391i | 0.993766 | − | 0.111490i | \(-0.0355624\pi\) |
−0.593436 | + | 0.804881i | \(0.702229\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 8.68951i | − | 0.622269i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.5150i | 1.53288i | 0.642317 | + | 0.766439i | \(0.277973\pi\) | ||||
−0.642317 | + | 0.766439i | \(0.722027\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.12311 | − | 15.8017i | −0.646720 | − | 1.12015i | −0.983901 | − | 0.178712i | \(-0.942807\pi\) |
0.337182 | − | 0.941440i | \(-0.390526\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −17.3693 | + | 30.0845i | −1.22514 | + | 2.12200i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.23726 | + | 3.60109i | 0.435629 | + | 0.251511i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.6847 | − | 27.1666i | −1.09016 | − | 1.88821i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.71659i | 0.324703i | 0.986733 | + | 0.162352i | \(0.0519079\pi\) | ||||
−0.986733 | + | 0.162352i | \(0.948092\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −20.9263 | + | 12.0818i | −1.43384 | + | 0.827831i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.12311 | + | 1.94528i | −0.0765952 | + | 0.132667i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.6947 | − | 9.06134i | −1.06055 | − | 0.612309i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.93780 | − | 1.69614i | 0.197618 | − | 0.114095i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.75379 | 0.385302 | 0.192651 | − | 0.981267i | \(-0.438291\pi\) | ||||
0.192651 | + | 0.981267i | \(0.438291\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.0000 | −0.866667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.49139 | + | 4.90251i | −0.563593 | + | 0.325391i | −0.754586 | − | 0.656201i | \(-0.772163\pi\) |
0.190993 | + | 0.981591i | \(0.438829\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.3952 | + | 12.9299i | 1.47992 | + | 0.854429i | 0.999741 | − | 0.0227441i | \(-0.00724029\pi\) |
0.480174 | + | 0.877173i | \(0.340574\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.12311 | − | 14.0696i | 0.532162 | − | 0.921732i | −0.467133 | − | 0.884187i | \(-0.654713\pi\) |
0.999295 | − | 0.0375449i | \(-0.0119537\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.6155 | 1.13945 | 0.569727 | − | 0.821834i | \(-0.307049\pi\) | ||||
0.569727 | + | 0.821834i | \(0.307049\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.87689 | + | 3.25088i | 0.120901 | + | 0.209407i | 0.920123 | − | 0.391629i | \(-0.128088\pi\) |
−0.799222 | + | 0.601036i | \(0.794755\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.97175 | + | 1.13839i | 0.126488 | + | 0.0730277i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.56155 | + | 4.43674i | −0.162988 | + | 0.282303i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.56155 | − | 14.8290i | −0.542566 | − | 0.939753i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.9663i | 0.692186i | 0.938200 | + | 0.346093i | \(0.112492\pi\) | ||||
−0.938200 | + | 0.346093i | \(0.887508\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 6.78456i | − | 0.426542i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.12311 | + | 8.87348i | 0.320821 | + | 0.555679i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.2462 | + | 19.4790i | −0.701519 | + | 1.21507i | 0.266414 | + | 0.963859i | \(0.414161\pi\) |
−0.967933 | + | 0.251208i | \(0.919172\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −32.0335 | − | 18.4945i | −1.98282 | − | 1.14478i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.24621 | + | 10.8188i | 0.385158 | + | 0.667113i | 0.991791 | − | 0.127869i | \(-0.0408137\pi\) |
−0.606633 | + | 0.794982i | \(0.707480\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.49242 | −0.275967 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 49.0708i | 3.00309i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.2823 | + | 5.93649i | −0.626923 | + | 0.361954i | −0.779560 | − | 0.626328i | \(-0.784557\pi\) |
0.152636 | + | 0.988282i | \(0.451224\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.12311 | − | 8.87348i | 0.311207 | − | 0.539025i | −0.667417 | − | 0.744684i | \(-0.732600\pi\) |
0.978624 | + | 0.205658i | \(0.0659336\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.43495 | − | 1.40582i | −0.146833 | − | 0.0847742i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.29377 | + | 1.32431i | −0.137819 | + | 0.0795699i | −0.567324 | − | 0.823495i | \(-0.692021\pi\) |
0.429505 | + | 0.903064i | \(0.358688\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −62.7386 | −3.75606 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.9545 | + | 10.9434i | −1.12673 | + | 0.650518i | −0.943110 | − | 0.332480i | \(-0.892115\pi\) |
−0.183619 | + | 0.982997i | \(0.558781\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −13.4009 | − | 7.73704i | −0.793803 | − | 0.458303i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | − | 11.2583i | 0.382353 | − | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −32.0335 | + | 18.4945i | −1.87783 | + | 1.08417i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 10.3857i | − | 0.606736i | −0.952873 | − | 0.303368i | \(-0.901889\pi\) | ||
0.952873 | − | 0.303368i | \(-0.0981112\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.630683 | 0.0367198 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.24621 | + | 10.8188i | 0.362442 | + | 0.627768i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.52534 | + | 4.34475i | 0.435201 | + | 0.251264i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.6847 | − | 27.1666i | 0.901060 | − | 1.56068i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.43845 | − | 2.49146i | −0.0823652 | − | 0.142661i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 25.2791i | − | 1.44275i | −0.692543 | − | 0.721377i | \(-0.743510\pi\) | ||
0.692543 | − | 0.721377i | \(-0.256490\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.78456i | 0.385960i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.24621 | − | 10.8188i | −0.354190 | − | 0.613475i | 0.632789 | − | 0.774324i | \(-0.281910\pi\) |
−0.986979 | + | 0.160849i | \(0.948577\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.3693 | − | 17.9602i | 0.586108 | − | 1.01517i | −0.408628 | − | 0.912701i | \(-0.633993\pi\) |
0.994736 | − | 0.102468i | \(-0.0326741\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.58184 | + | 2.06798i | 0.201176 | + | 0.116149i | 0.597204 | − | 0.802089i | \(-0.296278\pi\) |
−0.396028 | + | 0.918238i | \(0.629612\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.00000 | − | 6.92820i | −0.223957 | − | 0.387905i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −42.7386 | −2.38544 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 6.04090i | − | 0.336124i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.11863 | − | 1.80054i | 0.172991 | − | 0.0998762i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −27.3693 | + | 47.4050i | −1.51353 | + | 2.62151i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.8981 | − | 7.44672i | −0.708943 | − | 0.409309i | 0.101726 | − | 0.994812i | \(-0.467563\pi\) |
−0.810670 | + | 0.585504i | \(0.800897\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −32.0335 | + | 18.4945i | −1.75542 | + | 1.01349i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 19.5076 | 1.06581 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.876894 | −0.0477675 | −0.0238837 | − | 0.999715i | \(-0.507603\pi\) | ||||
−0.0238837 | + | 0.999715i | \(0.507603\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.7569 | + | 7.36520i | −0.692860 | + | 0.400023i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.7512 | − | 6.78456i | −0.636364 | − | 0.367405i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −13.1231 | + | 22.7299i | −0.706524 | + | 1.22374i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.02249 | − | 4.05444i | 0.376987 | − | 0.217654i | −0.299520 | − | 0.954090i | \(-0.596826\pi\) |
0.676507 | + | 0.736437i | \(0.263493\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 27.3471i | − | 1.46385i | −0.681383 | − | 0.731927i | \(-0.738621\pi\) | ||
0.681383 | − | 0.731927i | \(-0.261379\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.0000 | −0.854017 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.87689 | − | 6.71498i | −0.206346 | − | 0.357402i | 0.744215 | − | 0.667941i | \(-0.232824\pi\) |
−0.950561 | + | 0.310538i | \(0.899491\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.7512 | + | 6.78456i | 0.623689 | + | 0.360087i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.6847 | + | 27.1666i | −0.827805 | + | 1.43380i | 0.0719522 | + | 0.997408i | \(0.477077\pi\) |
−0.899757 | + | 0.436392i | \(0.856256\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.93845 | − | 8.55364i | −0.259918 | − | 0.450192i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 27.9277i | − | 1.46582i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.1768i | 0.532680i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.12311 | + | 8.87348i | 0.267424 | + | 0.463192i | 0.968196 | − | 0.250194i | \(-0.0804943\pi\) |
−0.700772 | + | 0.713385i | \(0.747161\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.0000 | − | 22.5167i | 0.676753 | − | 1.17217i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.7569 | − | 7.36520i | −0.660528 | − | 0.381356i | 0.131950 | − | 0.991256i | \(-0.457876\pi\) |
−0.792478 | + | 0.609901i | \(0.791209\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 18.2462 | + | 31.6034i | 0.942230 | + | 1.63199i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.2462 | 0.527707 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 36.4084i | − | 1.87017i | −0.354418 | − | 0.935087i | \(-0.615321\pi\) | ||
0.354418 | − | 0.935087i | \(-0.384679\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 34.3272 | − | 19.8188i | 1.75864 | − | 1.01535i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.24621 | + | 3.89055i | −0.114776 | + | 0.198798i | −0.917690 | − | 0.397297i | \(-0.869948\pi\) |
0.802914 | + | 0.596095i | \(0.203282\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.02249 | + | 4.05444i | 0.356973 | + | 0.206099i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −21.5703 | + | 12.4536i | −1.09366 | + | 0.631424i | −0.934548 | − | 0.355837i | \(-0.884196\pi\) |
−0.159110 | + | 0.987261i | \(0.550863\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.2462 | −0.518173 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 37.6155 | 1.89745 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.8076 | + | 10.2812i | 0.893740 | + | 0.516001i | 0.875164 | − | 0.483826i | \(-0.160753\pi\) |
0.0185761 | + | 0.999827i | \(0.494087\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.438447 | − | 0.759413i | 0.0218950 | − | 0.0379233i | −0.854870 | − | 0.518842i | \(-0.826363\pi\) |
0.876765 | + | 0.480919i | \(0.159697\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.0507 | − | 8.68951i | 0.749727 | − | 0.432855i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 17.1702i | − | 0.853195i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.00000 | −0.396545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.0000 | − | 22.5167i | −0.642809 | − | 1.11338i | −0.984803 | − | 0.173675i | \(-0.944436\pi\) |
0.341994 | − | 0.939702i | \(-0.388898\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −42.4966 | − | 24.5354i | −2.09620 | − | 1.21024i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.80776 | + | 8.32729i | −0.236004 | + | 0.408771i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.5616 | + | 21.7572i | 0.615142 | + | 1.06546i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.9277i | 1.36436i | 0.731185 | + | 0.682179i | \(0.238967\pi\) | ||||
−0.731185 | + | 0.682179i | \(0.761033\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 26.8122i | − | 1.30675i | −0.757036 | − | 0.653373i | \(-0.773353\pi\) | ||
0.757036 | − | 0.653373i | \(-0.226647\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.12311 | + | 3.67733i | −0.102986 | + | 0.178377i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.87560 | − | 3.39228i | −0.283677 | − | 0.163781i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.80776 | + | 15.2555i | 0.424255 | + | 0.734831i | 0.996351 | − | 0.0853557i | \(-0.0272027\pi\) |
−0.572095 | + | 0.820187i | \(0.693869\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.4924 | −0.888689 | −0.444345 | − | 0.895856i | \(-0.646563\pi\) | ||||
−0.444345 | + | 0.895856i | \(0.646563\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 30.9481i | 1.48385i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.4009 | − | 7.73704i | 0.641054 | − | 0.370113i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.3693 | − | 19.6922i | 0.542628 | − | 0.939859i | −0.456124 | − | 0.889916i | \(-0.650763\pi\) |
0.998752 | − | 0.0499429i | \(-0.0159039\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.37845 | + | 3.68260i | 0.303049 | + | 0.174966i | 0.643812 | − | 0.765184i | \(-0.277352\pi\) |
−0.340763 | + | 0.940149i | \(0.610685\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23.8641 | − | 13.7779i | 1.13127 | − | 0.653137i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 44.4924 | 2.10442 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.7386 | 0.789945 | 0.394972 | − | 0.918693i | \(-0.370754\pi\) | ||||
0.394972 | + | 0.918693i | \(0.370754\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.86991 | − | 2.81164i | 0.229315 | − | 0.132395i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −28.4516 | − | 16.4265i | −1.33677 | − | 0.771786i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.68466 | + | 15.0423i | −0.406251 | + | 0.703648i | −0.994466 | − | 0.105057i | \(-0.966498\pi\) |
0.588215 | + | 0.808705i | \(0.299831\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 16.3387 | − | 9.43318i | 0.762627 | − | 0.440303i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 24.3724i | − | 1.13514i | −0.823327 | − | 0.567568i | \(-0.807885\pi\) | ||
0.823327 | − | 0.567568i | \(-0.192115\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 26.2462 | + | 45.4598i | 1.21714 | + | 2.10815i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.61578 | + | 1.51022i | 0.121044 | + | 0.0698848i | 0.559300 | − | 0.828966i | \(-0.311070\pi\) |
−0.438255 | + | 0.898850i | \(0.644403\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.8078 | + | 22.1837i | −0.590151 | + | 1.02217i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.876894 | + | 1.51883i | 0.0403196 | + | 0.0698357i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 6.41273i | − | 0.294236i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.2177i | 0.742559i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.12311 | + | 8.87348i | 0.234081 | + | 0.405440i | 0.959005 | − | 0.283389i | \(-0.0914587\pi\) |
−0.724924 | + | 0.688828i | \(0.758125\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.12311 | − | 8.87348i | 0.233594 | − | 0.404596i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.9885 | + | 10.3857i | 0.816815 | + | 0.471588i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.315342 | + | 0.546188i | 0.0142895 | + | 0.0247501i | 0.873082 | − | 0.487574i | \(-0.162118\pi\) |
−0.858792 | + | 0.512324i | \(0.828785\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 40.4924 | 1.83113 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.1774i | 1.54240i | 0.636590 | + | 0.771202i | \(0.280344\pi\) | ||||
−0.636590 | + | 0.771202i | \(0.719656\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.4631 | + | 6.04090i | −0.471236 | + | 0.272068i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.87689 | − | 11.9111i | 0.309093 | − | 0.535366i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.66652 | + | 4.42627i | 0.343201 | + | 0.198147i | 0.661687 | − | 0.749781i | \(-0.269841\pi\) |
−0.318486 | + | 0.947928i | \(0.603174\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.9263 | − | 12.0818i | 0.934917 | − | 0.539775i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.7538 | −0.613251 | −0.306626 | − | 0.951830i | \(-0.599200\pi\) | ||||
−0.306626 | + | 0.951830i | \(0.599200\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.6155 | −0.783881 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −26.4799 | + | 15.2882i | −1.17601 | + | 0.678971i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −26.6211 | − | 15.3697i | −1.17996 | − | 0.681249i | −0.223953 | − | 0.974600i | \(-0.571896\pi\) |
−0.956005 | + | 0.293351i | \(0.905229\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −14.2462 | + | 24.6752i | −0.628986 | + | 1.08944i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.29946 | − | 1.90495i | 0.145392 | − | 0.0839419i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 57.6155 | 2.52904 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.0000 | + | 19.0526i | 0.481919 | + | 0.834708i | 0.999785 | − | 0.0207541i | \(-0.00660670\pi\) |
−0.517866 | + | 0.855462i | \(0.673273\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.6549 | + | 20.5854i | 1.55908 | + | 0.900136i | 0.997345 | + | 0.0728196i | \(0.0231997\pi\) |
0.561736 | + | 0.827316i | \(0.310134\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.2462 | + | 17.7470i | −0.446332 | + | 0.773070i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.62311 | − | 2.81130i | −0.0705698 | − | 0.122230i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 2.27678i | − | 0.0988038i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.20217i | 0.311961i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.0000 | + | 20.7846i | 0.518805 | + | 0.898597i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.12311 | + | 12.3376i | −0.307385 | + | 0.532406i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.4688 | − | 6.62153i | −0.493084 | − | 0.284682i | 0.232769 | − | 0.972532i | \(-0.425221\pi\) |
−0.725853 | + | 0.687850i | \(0.758555\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.5616 | − | 18.2931i | −0.453240 | − | 0.785034i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 30.7386 | 1.31670 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.59621i | 0.410304i | 0.978730 | + | 0.205152i | \(0.0657689\pi\) | ||||
−0.978730 | + | 0.205152i | \(0.934231\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.99424 | + | 5.19283i | −0.383865 | + | 0.221624i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.12311 | − | 15.8017i | 0.388657 | − | 0.673174i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 26.8019 | + | 15.4741i | 1.13768 | + | 0.656838i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.29377 | − | 1.32431i | 0.0971900 | − | 0.0561127i | −0.450617 | − | 0.892717i | \(-0.648796\pi\) |
0.547807 | + | 0.836605i | \(0.315463\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.24621 | −0.0950046 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00000 | 0.337760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.8358 | − | 14.9163i | 1.08885 | − | 0.628648i | 0.155580 | − | 0.987823i | \(-0.450275\pi\) |
0.933270 | + | 0.359175i | \(0.116942\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.16368 | + | 4.13595i | 0.301378 | + | 0.174001i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.68466 | − | 11.5782i | 0.280235 | − | 0.485382i | −0.691207 | − | 0.722657i | \(-0.742921\pi\) |
0.971443 | + | 0.237275i | \(0.0762541\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.02818 | + | 4.63507i | −0.335969 | + | 0.193972i | −0.658488 | − | 0.752591i | \(-0.728804\pi\) |
0.322519 | + | 0.946563i | \(0.395470\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 48.3272i | 2.01890i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.8769 | −0.453598 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.87689 | − | 6.71498i | −0.161397 | − | 0.279548i | 0.773973 | − | 0.633219i | \(-0.218267\pi\) |
−0.935370 | + | 0.353671i | \(0.884933\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −29.0956 | − | 16.7984i | −1.20917 | − | 0.698117i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.75379 | + | 3.03765i | −0.0726345 | + | 0.125807i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.80776 | + | 15.2555i | 0.364156 | + | 0.630737i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 21.8868i | − | 0.903365i | −0.892179 | − | 0.451683i | \(-0.850824\pi\) | ||
0.892179 | − | 0.451683i | \(-0.149176\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 30.9481i | − | 1.27520i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −32.4924 | − | 56.2785i | −1.33656 | − | 2.31499i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.00000 | + | 15.5885i | −0.369586 | + | 0.640141i | −0.989501 | − | 0.144528i | \(-0.953834\pi\) |
0.619915 | + | 0.784669i | \(0.287167\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 47.7282 | + | 27.5559i | 1.95338 | + | 1.12779i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.24621 | − | 10.8188i | −0.255213 | − | 0.442042i | 0.709740 | − | 0.704464i | \(-0.248812\pi\) |
−0.964953 | + | 0.262421i | \(0.915479\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.2462 | −0.662697 | −0.331348 | − | 0.943508i | \(-0.607504\pi\) | ||||
−0.331348 | + | 0.943508i | \(0.607504\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 70.4228i | − | 2.86784i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.5818 | + | 7.84144i | −0.552178 | + | 0.318800i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.4924 | − | 35.4939i | 0.831762 | − | 1.44065i | −0.0648782 | − | 0.997893i | \(-0.520666\pi\) |
0.896640 | − | 0.442760i | \(-0.146001\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.93211 | − | 1.11550i | 0.0780371 | − | 0.0450547i | −0.460474 | − | 0.887673i | \(-0.652320\pi\) |
0.538511 | + | 0.842619i | \(0.318987\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −21.7538 | −0.877197 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.3693 | −1.18236 | −0.591182 | − | 0.806538i | \(-0.701339\pi\) | ||||
−0.591182 | + | 0.806538i | \(0.701339\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.0224 | − | 9.82790i | 0.684189 | − | 0.395017i | −0.117243 | − | 0.993103i | \(-0.537405\pi\) |
0.801431 | + | 0.598087i | \(0.204072\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 41.8526 | + | 24.1636i | 1.67949 | + | 0.969651i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.93845 | − | 8.55364i | 0.197538 | − | 0.342146i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.4631 | + | 6.04090i | −0.417858 | + | 0.241250i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.0818i | 0.481733i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.50758 | 0.139634 | 0.0698172 | − | 0.997560i | \(-0.477758\pi\) | ||||
0.0698172 | + | 0.997560i | \(0.477758\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.12311 | − | 12.3376i | −0.283118 | − | 0.490375i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.2765 | − | 11.1293i | −0.764966 | − | 0.441654i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24.4924 | − | 42.4221i | 0.968905 | − | 1.67819i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.68466 | + | 4.64996i | 0.106038 | + | 0.183663i | 0.914162 | − | 0.405350i | \(-0.132850\pi\) |
−0.808124 | + | 0.589012i | \(0.799517\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.66906i | 0.223566i | 0.993733 | + | 0.111783i | \(0.0356562\pi\) | ||||
−0.993733 | + | 0.111783i | \(0.964344\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 6.78456i | − | 0.267142i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.6155 | + | 37.4392i | 0.849794 | + | 1.47189i | 0.881392 | + | 0.472386i | \(0.156607\pi\) |
−0.0315977 | + | 0.999501i | \(0.510060\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.246211 | − | 0.426450i | 0.00966464 | − | 0.0167396i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27.4459 | − | 15.8459i | −1.07404 | − | 0.620098i | −0.144759 | − | 0.989467i | \(-0.546241\pi\) |
−0.929283 | + | 0.369369i | \(0.879574\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.5616 | − | 18.2931i | −0.412674 | − | 0.714772i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 36.7386 | 1.43331 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.62153i | 0.257938i | 0.991649 | + | 0.128969i | \(0.0411668\pi\) | ||||
−0.991649 | + | 0.128969i | \(0.958833\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.7339 | − | 22.3630i | 1.50657 | − | 0.869821i | 0.506604 | − | 0.862179i | \(-0.330901\pi\) |
0.999971 | − | 0.00764267i | \(-0.00243276\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.12311 | + | 8.87348i | −0.198965 | + | 0.344617i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −26.8019 | − | 15.4741i | −1.03777 | − | 0.599159i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.0507 | + | 8.68951i | −0.581893 | + | 0.335956i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.24621 | −0.0867140 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −38.9848 | −1.50276 | −0.751378 | − | 0.659872i | \(-0.770610\pi\) | ||||
−0.751378 | + | 0.659872i | \(0.770610\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17.3444 | − | 10.0138i | 0.667588 | − | 0.385432i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.8698 | + | 8.58511i | 0.571494 | + | 0.329952i | 0.757746 | − | 0.652550i | \(-0.226301\pi\) |
−0.186252 | + | 0.982502i | \(0.559634\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.8078 | − | 25.6478i | 0.567435 | − | 0.982826i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.502848 | + | 0.290319i | −0.0192409 | + | 0.0111088i | −0.509590 | − | 0.860418i | \(-0.670203\pi\) |
0.490349 | + | 0.871526i | \(0.336869\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 27.5559i | 1.05286i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −78.1080 | −2.98000 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.24621 | − | 3.89055i | −0.0855738 | − | 0.148218i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.6435 | + | 19.4241i | 1.27986 | + | 0.738928i | 0.976823 | − | 0.214051i | \(-0.0686657\pi\) |
0.303038 | + | 0.952978i | \(0.401999\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.05398 | − | 12.2178i | 0.267573 | − | 0.463449i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.24621 | − | 7.35465i | −0.160837 | − | 0.278577i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 49.0708i | 1.85603i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 2.23100i | − | 0.0842639i | −0.999112 | − | 0.0421319i | \(-0.986585\pi\) | ||
0.999112 | − | 0.0421319i | \(-0.0134150\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.12311 | − | 15.8017i | −0.344084 | − | 0.595972i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.8698 | + | 14.3586i | 0.934004 | + | 0.539247i | 0.888076 | − | 0.459697i | \(-0.152042\pi\) |
0.0459283 | + | 0.998945i | \(0.485375\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −52.4924 | −1.96586 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.80989i | 0.142482i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −46.0784 | + | 26.6034i | −1.72083 | + | 0.993522i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.2462 | + | 45.4598i | −0.978819 | + | 1.69536i | −0.312108 | + | 0.950047i | \(0.601035\pi\) |
−0.666711 | + | 0.745317i | \(0.732298\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.81910 | − | 5.66906i | −0.365176 | − | 0.210835i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11.1072 | + | 6.41273i | −0.412510 | + | 0.238163i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.9848 | 0.629933 | 0.314967 | − | 0.949103i | \(-0.398007\pi\) | ||||
0.314967 | + | 0.949103i | \(0.398007\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.4924 | 0.870090 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.29377 | − | 1.32431i | 0.0848380 | − | 0.0489813i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.3330 | + | 14.6260i | 0.935695 | + | 0.540224i | 0.888608 | − | 0.458667i | \(-0.151673\pi\) |
0.0470868 | + | 0.998891i | \(0.485006\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.61553 | − | 13.1905i | 0.280522 | − | 0.485878i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.4913 | + | 10.6760i | −0.680214 | + | 0.392722i | −0.799936 | − | 0.600086i | \(-0.795133\pi\) |
0.119721 | + | 0.992808i | \(0.461800\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 15.4741i | − | 0.568454i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.630683 | −0.0231375 | −0.0115688 | − | 0.999933i | \(-0.503683\pi\) | ||||
−0.0115688 | + | 0.999933i | \(0.503683\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.4924 | − | 21.6375i | −0.457687 | − | 0.792737i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 30.0617 | + | 17.3561i | 1.09990 | + | 0.635028i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.31534 | − | 7.47439i | 0.157469 | − | 0.272744i | −0.776486 | − | 0.630134i | \(-0.783000\pi\) |
0.933955 | + | 0.357390i | \(0.116333\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16.5616 | − | 28.6855i | −0.603537 | − | 1.04536i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.4487i | 0.671419i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.3946i | 0.959328i | 0.877452 | + | 0.479664i | \(0.159241\pi\) | ||||
−0.877452 | + | 0.479664i | \(0.840759\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.2462 | + | 17.7470i | 0.371914 | + | 0.644174i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.36932 | + | 7.56788i | −0.158388 | + | 0.274335i | −0.934287 | − | 0.356521i | \(-0.883963\pi\) |
0.775900 | + | 0.630856i | \(0.217296\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −17.9885 | − | 10.3857i | −0.650375 | − | 0.375494i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.315342 | + | 0.546188i | 0.0113863 | + | 0.0197217i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40.2462 | −1.45132 | −0.725658 | − | 0.688056i | \(-0.758464\pi\) | ||||
−0.725658 | + | 0.688056i | \(0.758464\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 67.9372i | − | 2.44670i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.46890 | + | 0.848071i | −0.0528327 | + | 0.0305030i | −0.526184 | − | 0.850371i | \(-0.676378\pi\) |
0.473351 | + | 0.880874i | \(0.343044\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.8769 | + | 18.8393i | −0.390710 | + | 0.676729i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.1072 | + | 6.41273i | 0.397956 | + | 0.229760i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.17507 | − | 5.29723i | 0.328310 | − | 0.189550i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 56.9848 | 2.03647 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.3845 | 0.513404 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.13543 | − | 5.27434i | 0.325643 | − | 0.188010i | −0.328262 | − | 0.944587i | \(-0.606463\pi\) |
0.653905 | + | 0.756577i | \(0.273130\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −32.6775 | − | 18.8664i | −1.16335 | − | 0.671660i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.43845 | − | 2.49146i | 0.0510808 | − | 0.0884745i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 11.7512 | − | 6.78456i | 0.416772 | − | 0.240624i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.8597i | 0.915998i | 0.888953 | + | 0.457999i | \(0.151434\pi\) | ||||
−0.888953 | + | 0.457999i | \(0.848566\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −49.7386 | − | 86.1498i | −1.75743 | − | 3.04395i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.88130 | + | 3.97292i | 0.242836 | + | 0.140201i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.9309 | − | 31.0572i | 0.631197 | − | 1.09326i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.9309 | − | 32.7892i | −0.665574 | − | 1.15281i | −0.979129 | − | 0.203238i | \(-0.934853\pi\) |
0.313555 | − | 0.949570i | \(-0.398480\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.8459i | 0.556425i | 0.960520 | + | 0.278213i | \(0.0897420\pi\) | ||||
−0.960520 | + | 0.278213i | \(0.910258\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 30.9481i | 1.08540i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.3693 | − | 19.6922i | −0.398250 | − | 0.689789i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.00000 | + | 3.46410i | −0.0699711 | + | 0.121194i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.0956 | + | 16.7984i | 1.01545 | + | 0.586268i | 0.912781 | − | 0.408449i | \(-0.133930\pi\) |
0.102664 | + | 0.994716i | \(0.467263\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.4924 | − | 28.5657i | −0.574890 | − | 0.995738i | −0.996054 | − | 0.0887536i | \(-0.971712\pi\) |
0.421164 | − | 0.906985i | \(-0.361622\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.49242 | 0.295668 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.20393i | 0.215732i | 0.994165 | + | 0.107866i | \(0.0344017\pi\) | ||||
−0.994165 | + | 0.107866i | \(0.965598\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −40.3837 | + | 23.3155i | −1.40258 | + | 0.809781i | −0.994657 | − | 0.103234i | \(-0.967081\pi\) |
−0.407925 | + | 0.913015i | \(0.633748\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.00000 | − | 6.92820i | 0.138758 | − | 0.240337i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.7512 | − | 6.78456i | −0.406667 | − | 0.234790i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 83.7051 | − | 48.3272i | 2.89327 | − | 1.67043i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.73863 | 0.232643 | 0.116322 | − | 0.993212i | \(-0.462890\pi\) | ||||
0.116322 | + | 0.993212i | \(0.462890\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.49242 | −0.258359 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.6947 | − | 9.06134i | 0.540554 | − | 0.312089i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.8698 | + | 8.58511i | 0.511538 | + | 0.295337i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 33.0540 | − | 57.2512i | 1.13441 | − | 1.96485i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26.8019 | + | 15.4741i | −0.918757 | + | 0.530444i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.4421i | 0.871121i | 0.900159 | + | 0.435561i | \(0.143450\pi\) | ||||
−0.900159 | + | 0.435561i | \(0.856550\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 31.3693 | 1.07281 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.4924 | + | 40.6901i | 0.802486 | + | 1.38995i | 0.917975 | + | 0.396638i | \(0.129823\pi\) |
−0.115489 | + | 0.993309i | \(0.536844\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.5478 | − | 14.1727i | −0.837559 | − | 0.483565i | 0.0188750 | − | 0.999822i | \(-0.493992\pi\) |
−0.856434 | + | 0.516257i | \(0.827325\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.2462 | − | 31.6034i | 0.621108 | − | 1.07579i | −0.368171 | − | 0.929758i | \(-0.620016\pi\) |
0.989280 | − | 0.146033i | \(-0.0466506\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.1771 | − | 28.0195i | −0.550037 | − | 0.952692i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 39.2658i | 1.33354i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.75379 | + | 16.8941i | 0.330495 | + | 0.572433i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 37.4924 | − | 64.9388i | 1.26893 | − | 2.19784i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.7454 | − | 17.7509i | −1.03820 | − | 0.599404i | −0.118875 | − | 0.992909i | \(-0.537929\pi\) |
−0.919322 | + | 0.393505i | \(0.871262\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.6847 | + | 27.1666i | 0.529030 | + | 0.916308i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.2462 | 1.49069 | 0.745346 | − | 0.666677i | \(-0.232284\pi\) | ||||
0.745346 | + | 0.666677i | \(0.232284\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.71659i | 0.158726i | 0.996846 | + | 0.0793629i | \(0.0252886\pi\) | ||||
−0.996846 | + | 0.0793629i | \(0.974711\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.64973 | + | 0.952473i | −0.0554551 | + | 0.0320170i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.2462 | + | 24.6752i | −0.478341 | + | 0.828511i | −0.999692 | − | 0.0248317i | \(-0.992095\pi\) |
0.521351 | + | 0.853343i | \(0.325428\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.6100 | − | 6.70305i | −0.388950 | − | 0.224561i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.00000 | 0.267411 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −26.2462 | −0.876335 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −53.6038 | + | 30.9481i | −1.78779 | + | 1.03218i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.58753 | + | 2.64861i | 0.152833 | + | 0.0882381i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.93087 | + | 10.2726i | −0.197149 | + | 0.341472i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 44.6492 | − | 25.7782i | 1.48255 | − | 0.855951i | 0.482748 | − | 0.875760i | \(-0.339639\pi\) |
0.999804 | + | 0.0198082i | \(0.00630555\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 63.5924i | 2.10923i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.8617 | −0.392997 | −0.196498 | − | 0.980504i | \(-0.562957\pi\) | ||||
−0.196498 | + | 0.980504i | \(0.562957\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.75379 | + | 6.50175i | 0.124232 | + | 0.215177i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.52534 | + | 4.34475i | 0.248780 | + | 0.143633i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.00000 | − | 6.92820i | 0.131948 | − | 0.228540i | −0.792480 | − | 0.609898i | \(-0.791210\pi\) |
0.924427 | + | 0.381358i | \(0.124544\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 38.1771 | + | 66.1246i | 1.25798 | + | 2.17888i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.5691i | 0.446633i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.8255i | 0.421699i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.87689 | − | 11.9111i | −0.225867 | − | 0.391213i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.24621 | − | 2.15850i | 0.0408869 | − | 0.0708181i | −0.844858 | − | 0.534991i | \(-0.820315\pi\) |
0.885745 | + | 0.464173i | \(0.153648\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 32.6775 | + | 18.8664i | 1.06981 | + | 0.617657i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.24621 | − | 3.89055i | −0.0734590 | − | 0.127235i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.9848 | 1.14291 | 0.571453 | − | 0.820635i | \(-0.306380\pi\) | ||||
0.571453 | + | 0.820635i | \(0.306380\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 62.6400i | 2.04418i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.6211 | − | 15.3697i | 0.867821 | − | 0.501037i | 0.00119780 | − | 0.999999i | \(-0.499619\pi\) |
0.866624 | + | 0.498962i | \(0.166285\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.8769 | − | 18.8393i | 0.354200 | − | 0.613493i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.1181 | + | 20.8528i | 1.17368 | + | 0.677625i | 0.954544 | − | 0.298069i | \(-0.0963424\pi\) |
0.219137 | + | 0.975694i | \(0.429676\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.81341 | + | 5.08842i | −0.286095 | + | 0.165177i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.4924 | −0.405095 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.5076 | −0.567126 | −0.283563 | − | 0.958954i | \(-0.591517\pi\) | ||||
−0.283563 | + | 0.958954i | \(0.591517\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.5024 | − | 13.5691i | 0.760520 | − | 0.439087i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.9263 | + | 12.0818i | 0.676450 | + | 0.390549i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −36.9924 | + | 64.0728i | −1.19330 | + | 2.06686i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 75.0329 | − | 43.3203i | 2.41790 | − | 1.39598i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 18.8664i | 0.607329i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.8769 | 0.349777 | 0.174889 | − | 0.984588i | \(-0.444043\pi\) | ||||
0.174889 | + | 0.984588i | \(0.444043\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.12311 | + | 15.8017i | 0.293076 | + | 0.507623i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.49709 | − | 5.48314i | −0.304776 | − | 0.175962i | 0.339810 | − | 0.940494i | \(-0.389637\pi\) |
−0.644586 | + | 0.764531i | \(0.722970\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.43845 | + | 9.41967i | −0.174170 | + | 0.301671i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.8769 | − | 20.5714i | −0.379976 | − | 0.658137i | 0.611083 | − | 0.791567i | \(-0.290734\pi\) |
−0.991058 | + | 0.133430i | \(0.957401\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 21.5150i | − | 0.687621i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 110.967i | − | 3.54291i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.1231 | − | 29.6581i | −0.546142 | − | 0.945946i | −0.998534 | − | 0.0541268i | \(-0.982762\pi\) |
0.452392 | − | 0.891819i | \(-0.350571\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.2462 | + | 31.6034i | −0.581373 | + | 1.00697i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.87560 | + | 3.39228i | 0.186833 | + | 0.107868i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.2462 | − | 31.6034i | −0.579610 | − | 1.00391i | −0.995524 | − | 0.0945100i | \(-0.969872\pi\) |
0.415914 | − | 0.909404i | \(-0.363462\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 44.9848 | 1.42755 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 30.9481i | − | 0.981122i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.6324 | − | 16.5309i | 0.906799 | − | 0.523540i | 0.0273989 | − | 0.999625i | \(-0.491278\pi\) |
0.879400 | + | 0.476084i | \(0.157944\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 28.4924 | − | 49.3503i | 0.901460 | − | 1.56138i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))